Auctions frequently utilize a buyer’s premium, which is a percentage of the final bid price, added to such to then calculate the final sales price. For example, a car selling at auction for $15,000 with a 10% buyer’s premium would then require the buyer to tender $15,000 + (.10*15000) = $16,500.

We wrote about Buyer’s Premiums and how they worked some time ago. This article is about how to calculate the buyer’s premium.

There is the conventional manner in which this calculation is completed, as we noted above. Most everyone takes the final hammer price times the buyer’s premium, and then adds the final hammer price. While this method is acceptable, there is an easier way to do this calculation if one has a calculator handy.

Our quicker method involves the principle that adding a percentage to a number is the same as multiplying it by [1+that percentage]. For example, adding 10% is the same as multiplying by 1.10 where “10%” is expressed as the decimal “.10″

Therefore, when adding a buyer’s premium, convert the buyer’s premium to a decimal, and add it to 1 and multiply the final bid by this number for the total including the buyer’s premium. Some examples:

Let’s move on to calculating what the high bid was, if we know the number which includes the buyer’s premium.

For example, someone says that a John Deere tractor recently sold at auction for $60,500 including a 10% buyer’s premium. How would we figure what the hammer price was?

By taking the $60,500 total price for the John Deere tractor, and dividing by 1.10 we get $55,000, which must have been the high bid, prior to adding the buyer’s premium.

Therefore, when backing out a buyer’s premium, convert the buyer’s premium to a decimal, and add it to 1 and divide the total price by this number for the high bid excluding the buyer’s premium. Some examples:

Lastly, how is just the buyer’s premium calculated, based upon either the high bid price, or the total sales price including the buyer’s premium?

If the high bid price is known, the buyer’s premium is calculated by taking the buyer’s premium as a percentage times the high bid price. For example, a diamond ring sells for $4,900 and a 10% buyer’s premium is charged. The buyer’s premium alone would be 4,900*.10 = $490.

If the total sales price is known, including the buyer’s premium, we can calculate what the buyer’s premium was by taking the total sales price times [buyer’s premium / 1+buyer’s premium]. For example, our aforementioned diamond ring sells for $5,390 including a 10% buyer’s premium. If we want to know how much the buyer’s premium was, we take 5,390*.10/1.10 = $490. Some other examples:

A common miscalculation occurs when buyer’s premiums are used. A typical example of this miscalculation:

Frank sells his home for a high bid price of $162,000, plus 10% buyer’s premium. Therefore, using our above formulas, we take 162,000*1.10 = $178,200. At the closing, the title agent figures that since a 10% buyer’s premium was charged, he can take 10% of $178,200 and give that to the auctioneer. That would be $178,200 * .10 = $17,820.

However, if we subtract this $17,820 from the total sales price of $178,200, we get $160,380, which is not the high bid price the seller is entitled to receive. To calculate the buyer’s premium correctly, he should take $178,200 *.10 / 1.10 = $16,200. That would leave our seller the balance of $178,200 – $16,200 = $162,000.

This miscalculation, if not caught, would cost the seller $1,620 more in commission, and profit the auctioneer the same in additional commission. The error is a result of taking the commission as a percentage of the total sales price, which in effect, causes the commission to be calculated on top of a figure already containing commission.

Care must be taken to ensure the buyer’s premium numbers are calculated correctly.